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Elements of Relativity Theory

D. F. Lawden
Dover Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
, on

This is an unabridged republication by Dover Publications of a 1985 text. Much of the material is expanded and updated in more recent editions of the author’s Introduction to Tensor Calculus, Relativity and Cosmology, also published by Dover. This a gentler, briefer introduction focusing mostly on the basic concepts of special relativity theory. The fundamentals of special relativity are conveyed in examples and exercises over four of the work’s five chapters. A first semester in calculus and university physics is sufficient for the text and exercises. The lesson-like material is suitable for undergraduates and first-year graduate students.

The text begins with vector basics, establishing the definition of inertial frames, and a few fundamental axioms of special relativity. Thus the first chapters quickly move from Newtonian mechanics to the scope and foundation of special relativity. In Chapter 2, the Lorentz Transformation Equations are derived and the material suggests a more remote antiquity: “If O is at rest in the aether…” While the work was originally published in 1985, it is based on lectures given by Lawden at the University of Aston from 1977 to 1983.

By the end of Chapter 2, Minkowski diagrams emerge and tachyons are set aside as an interesting curiosity. This chapter includes some of the more engaging examples and exercises, such as using the mathematics of length contraction to park a five-meter car cruising at 60% the speed of light into a four-meter garage. This text is rich in mathematics and the diligent reader will not only see that that this valet’s miracle is possible, but will calculate that in the driver’s frame, the garage is 3.2m long and the front bumper contacts the back wall 3/c before the doors may close.

Beside Fitzgerald Contraction, the Compton Effect of inelastic scattering of a photon by a charged particle and Planck’s Constant are also derived, not merely defined. This leaves room for a final chapter to introduce General Relativity focused on the mathematical models of gravity lensing, light reddening, and the tantalizing possibility of something called a “black hole”.

Tom Schulte first fell in love with the counterintuitive concepts of the relativistic universe with The Iron Sun: Crossing The Universe Through Black Holes, by Adrian Berry, first published 1977, and still enjoys classics of the literature.


1. Special Principle of Relativity.
2. Lorentz Transformation.
3. Velocity Transformations.
4. Relativistic Mechanics.
5. General Theory of Relativity.